DISTRIBUTIVE PROPERTY OF MULTIPLICATION WORKSHEETS

Problem 1 :

Evaluate using distributive property :

(i)  7(10 + 2)

(ii)  5(7 - 3)

(iii)  5(p + q)

(iv)  m(n - p)

(v)  5(a² + b² + c²)

(vi)  x(x² - x)

Problem 2 :

Write the given verbal phrase into algebraic expression

(i)  3 times the sum of two different numbers

(ii)  7 times the difference of 5 times of a number and 4.

(iii)  If 4 times the difference of a number and 5 is 32, find the number.

(iv)  If 7 times the sum of 3 times of a number and 6 is 147, find the number. 

Detailed Answer Key 

Problem 1 :

Evaluate using distributive property :

(i)  7(10 + 2)

Solution :

Use distributive property.

=  7(10) + 7(2)

=  70 + 14 

=  84

So, the value of 7(10 + 2) is 84.

(ii)  5(7 - 3)

Solution :

Use distributive property.

=  5(7) - 5(3)

=  35 - 15 

=  20

So, the value of 5(7 - 3) is 20.

(iii)  5(p + q)

Solution :

Use distributive property.

=  5p + 5q

(iv)  m(n - p)

Solution :

Use distributive property.

=  mn - mp

(vi)  5(a² + b² + c²)

Solution :

Use distributive property.

=  5a² + 5b² + 5c²

(vii)  x(x² - x)

Solution :

Use distributive property.

=  x ⋅ x² - x ⋅ x

=  x³ - x²

Problem 2 :

Write the given verbal phrase into algebraic expression

(i)  3 times the sum of two different numbers

Solution :

Let x and y be the two different numbers.

Then, 3 times the sum of two different numbers is 

=  3(x + y)

Use distributive property.

=  3x + 3y

(ii)  7 times the difference of 5 times of a number and 4"

Solution :

Let x and y be the two different numbers.

Then, 7 times the difference of 5 times of a number and 4 is

=  7(7x - 5)

Use distributive property.

=  49x - 35

(iii)  If 4 times the difference of a number and 5 is 32, find the number. 

Solution :

Let x be the number. 

Then,

4(x - 5)  =  32

Use distributive property. 

4x - 20  =  32

Add 20 to each side. 

4x  =  52

Divide each side by 4.

x  =  13

So, the number is 13. 

(iv)  If 7 times the sum of 3 times of a number and 6 is 147, find the number. 

Solution :

Let x be the number. 

Then,

7(3x + 6)  =  147

Use distributive property.

21x + 42  =  147

Subtract 42 from each side. 

21x  =  105

Divide each side by 21.

x  =  5

So, the number is 5. 

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